Costas Dimitrakopoulos - Academia.edu (original) (raw)
Books by Costas Dimitrakopoulos
Journal of Philosophical Research, 2015
The twenty-third World Congress of Philosophy was held in Athens in 2013. It was sponsored by the... more The twenty-third World Congress of Philosophy was held in Athens in 2013. It was sponsored by the Greek Philosophical Society, in cooperation with the Fédération Internationale des Sociétés de Philosophie. This volume contains outstanding papers presented at the plenary session, symposia, and Endowed Lecture sessions of this congress. It has been published in both print and electronic formats as a special supplement to the Journal of Philosophical Research. Print copies are also available from Amazon.
Papers by Costas Dimitrakopoulos
Archive for Mathematical Logic, Aug 1, 2000
The Wholeness Axiom (WA) is an axiom schema that can be added to the axioms of ZFC in an extended... more The Wholeness Axiom (WA) is an axiom schema that can be added to the axioms of ZFC in an extended language {∈, j}, and that asserts the existence of a nontrivial elementary embedding j : V → V. The well-known inconsistency proofs are avoided by omitting from the schema all instances of Replacement for j-formulas. We show that the theory ZFC + V = HOD + WA is consistent relative to the existence of an I 1 embedding. This answers a question about the existence of Laver sequences for regular classes of set embeddings: Assuming there is an I 1-embedding, there is a transitive model of ZFC+WA+ "there is a regular class of embeddings that admits no Laver sequence."
Journal of Symbolic Logic, Mar 1, 1993
Journal of Symbolic Logic, Jun 1, 1990
Journal of Logic and Computation, Aug 8, 2007
Metascience, Feb 6, 2013
The volume is a collection of papers concerning connections between reality and logic, where the ... more The volume is a collection of papers concerning connections between reality and logic, where the latter term is thought to refer to logical structures that are used to describe reality. Most of the papers included in the volume owe their present form to international conferences and/or scientific projects that were realized in Croatia in the last decade, with the active involvement of academics from all around the world. The book is composed of fifteen chapters, the first of which, authored by the editors of the volume, is an introduction to the other fourteen chapters, which are grouped into four parts. The first part contains chapters 2–5, which deal with foundational questions on logico-mathematical structures. In chapter 2, Stewart Shapiro studies the question how much mathematics should a philosopher of mathematics know to be able to do research in his discipline. After discussing shortly the main twentieth century schools in the philosophy of mathematics, that is, logicism, formalism and intuitionism, he considers this question in relation to work done in the area in the last two decades or so. Dale Jacquette, in the next chapter, deals with the problem of explaining the relation between pure and applied mathematics. After criticizing the solutions to this problem offered by all main streams in the philosophy of mathematics, he proposes a novel approach, which he calls ‘‘Aristotelian inherence metaphysics,’’ and argues that it provides satisfactory answers to the main questions confronting a philosophy of applied mathematics. The fourth chapter, authored by Milos Arsenijevic, concerns the philosophical impact of the Lowenheim-Skolem theorem, one of the landmark results on properties of models of first-order theories. The author gives a short presentation of the historical background, the generalizations and consequences of the theorem and then explains why this result follows from both the limitations of first-order logic and the language independence of the
Notre Dame Journal of Formal Logic, 2016
We give alternative proofs of results due to Paris and Wilkie concerning the existence of end ext... more We give alternative proofs of results due to Paris and Wilkie concerning the existence of end extensions of countable models of B † 1 , that is, the theory of † 1 collection.
Archive for Mathematical Logic, Aug 1, 1994
Metascience, Dec 24, 2014
Journal of Symbolic Logic, Jun 1, 1997
Journal of Symbolic Logic, Dec 1, 1988
We present a comprehensive study of the axiom schemas 127 ", B27" (induction and collection schem... more We present a comprehensive study of the axiom schemas 127 ", B27" (induction and collection schemas for parameter free Z" formulas) and some closely related schemas. Introduction. This paper is divided into three main sections. In §1 we investigate the relationship between IZ~, BZ~ and their parameter counterparts ll", BZ". In §2 we prove a series of conservation results which enable us to give axiomatizations of the Z" + 2 and Z n+l consequences of IZ". Finally, in §3 we investigate the quantifier complexity and finite axiomatizability of these schemas. §0. Preliminaries and summary of main results. We work in the usual first-order language of arithmetic {0,1, +, •, <}. P" denotes a finite set of 77, axioms such that if M 1= P~, then M is the nonnegative part of a commutative discretely ordered ring (see [4] for a precise definition of P~). II~ is P~ together with the schema 0(0) A Vx(0(x)-• 0(x + 1))-»'Vx0(x), 0 e Z". BZ~ is P" + ir 0 together with the schema Vx3y0(x,y)-»• VzBtVx < z3y < td(x,y), 0 e S". LS~ is P" together with the schema 3x0(x)-> 3x(0(x) A Vy < x-i0(y)), 6 e I B .
Logica Universalis, Apr 18, 2022
On the basis of recent work concerning the meaning of the term stoicheion ( στοιχεῖον ) in Aristo... more On the basis of recent work concerning the meaning of the term stoicheion ( στοιχεῖον ) in Aristotle’s Analytics , we strengthen the view that this treatise can be viewed as a precursor of Euclid’s Elements .
Abstract. We give a negative solution to the first part of Problem 4 in [1], i.e. we show that EA... more Abstract. We give a negative solution to the first part of Problem 4 in [1], i.e. we show that EA (=Elementary Arithmetic) does not imply the parameter free induction schema for decidable predicates, I ∆ − 1. 1
Logica Universalis
On the basis of recent work concerning the meaning of the term stoicheion ( στοιχεῖον ) in Aristo... more On the basis of recent work concerning the meaning of the term stoicheion ( στοιχεῖον ) in Aristotle’s Analytics , we strengthen the view that this treatise can be viewed as a precursor of Euclid’s Elements .
Computability in Europe (CiE) is an informal network of European scientists working on computabil... more Computability in Europe (CiE) is an informal network of European scientists working on computability theory, including its foundations, technical development, and applications. Among the aims of the network is to advance our theoretical understanding of what can and cannot be computed, by any means of computation. Its scientific vision is broad: computations may be performed with discrete or continuous data by all kinds of algorithms, programs, and machines. Computations may be made by experimenting with any sort of physical system obeying the laws of a physical theory such as Newtonian mechanics, quantum theory, or relativity. Computations may be very general, depending on the foundations of set theory; or very specific, using the combinatorics of finite structures. CiE also works on subjects intimately related to computation, especially theories of data and information, and methods for formal reasoning about computations. The sources of new ideas and methods include practical deve...
The field of weak arithmetics is an application of logical methods to number theory that was deve... more The field of weak arithmetics is an application of logical methods to number theory that was developed by mathematicians, philosophers, and theoretical computer scientists. New Studies in Weak Arithmetics is dedicated to late Australian mathematician Alan Robert Woods (1953-2011), whose seminal thesis is published here for the first time. This volume also contains the unpublished but significant thesis of Hamid Lesan (1951-2006) as well as other original papers on topics addressed in Woods' thesis and life's work that were first presented at the 31st Journees sur les Arithmetiques Faibles meeting held in Samos, Greece, in 2012.
1. Thread algebra and risk assessment services Jan A. Bergstra, Inge Bethke and Alban Ponse 2. Co... more 1. Thread algebra and risk assessment services Jan A. Bergstra, Inge Bethke and Alban Ponse 2. Covering definable manifolds by open definable subsets Mario J. Edmundo 3. Isomorphisms and definable relations on computable models Sergei S. Goncharov 4. Independence for types in algebraically closed valued fields Deirdre Haskell 5. Simple groups of finite Morley rank Eric Jaligot 6. Towards a logic of type-free modality and truth Hannes Leitgeb 7. Structural analysis of Aronszajn trees Justin Tatch Moore 8. Proof analysis in non-classical logics Sara Negri 9. Paul Bernays' later philosophy of mathematics Charles Parsons 10. Proofnets for S5: sequents and circuits for modal logic Greg Restall 11. Recursion on the partial continuous functionals Helmut Schwichtenberg 12. A transactional approach to the logic of truth Michael Sheard 13. On some problems in computable topology Dieter Spreen 14. Monotone inductive definitions and consistency of New Foundations Sergei Tupailo.
Journal of Philosophical Research, 2015
The twenty-third World Congress of Philosophy was held in Athens in 2013. It was sponsored by the... more The twenty-third World Congress of Philosophy was held in Athens in 2013. It was sponsored by the Greek Philosophical Society, in cooperation with the Fédération Internationale des Sociétés de Philosophie. This volume contains outstanding papers presented at the plenary session, symposia, and Endowed Lecture sessions of this congress. It has been published in both print and electronic formats as a special supplement to the Journal of Philosophical Research. Print copies are also available from Amazon.
Archive for Mathematical Logic, Aug 1, 2000
The Wholeness Axiom (WA) is an axiom schema that can be added to the axioms of ZFC in an extended... more The Wholeness Axiom (WA) is an axiom schema that can be added to the axioms of ZFC in an extended language {∈, j}, and that asserts the existence of a nontrivial elementary embedding j : V → V. The well-known inconsistency proofs are avoided by omitting from the schema all instances of Replacement for j-formulas. We show that the theory ZFC + V = HOD + WA is consistent relative to the existence of an I 1 embedding. This answers a question about the existence of Laver sequences for regular classes of set embeddings: Assuming there is an I 1-embedding, there is a transitive model of ZFC+WA+ "there is a regular class of embeddings that admits no Laver sequence."
Journal of Symbolic Logic, Mar 1, 1993
Journal of Symbolic Logic, Jun 1, 1990
Journal of Logic and Computation, Aug 8, 2007
Metascience, Feb 6, 2013
The volume is a collection of papers concerning connections between reality and logic, where the ... more The volume is a collection of papers concerning connections between reality and logic, where the latter term is thought to refer to logical structures that are used to describe reality. Most of the papers included in the volume owe their present form to international conferences and/or scientific projects that were realized in Croatia in the last decade, with the active involvement of academics from all around the world. The book is composed of fifteen chapters, the first of which, authored by the editors of the volume, is an introduction to the other fourteen chapters, which are grouped into four parts. The first part contains chapters 2–5, which deal with foundational questions on logico-mathematical structures. In chapter 2, Stewart Shapiro studies the question how much mathematics should a philosopher of mathematics know to be able to do research in his discipline. After discussing shortly the main twentieth century schools in the philosophy of mathematics, that is, logicism, formalism and intuitionism, he considers this question in relation to work done in the area in the last two decades or so. Dale Jacquette, in the next chapter, deals with the problem of explaining the relation between pure and applied mathematics. After criticizing the solutions to this problem offered by all main streams in the philosophy of mathematics, he proposes a novel approach, which he calls ‘‘Aristotelian inherence metaphysics,’’ and argues that it provides satisfactory answers to the main questions confronting a philosophy of applied mathematics. The fourth chapter, authored by Milos Arsenijevic, concerns the philosophical impact of the Lowenheim-Skolem theorem, one of the landmark results on properties of models of first-order theories. The author gives a short presentation of the historical background, the generalizations and consequences of the theorem and then explains why this result follows from both the limitations of first-order logic and the language independence of the
Notre Dame Journal of Formal Logic, 2016
We give alternative proofs of results due to Paris and Wilkie concerning the existence of end ext... more We give alternative proofs of results due to Paris and Wilkie concerning the existence of end extensions of countable models of B † 1 , that is, the theory of † 1 collection.
Archive for Mathematical Logic, Aug 1, 1994
Metascience, Dec 24, 2014
Journal of Symbolic Logic, Jun 1, 1997
Journal of Symbolic Logic, Dec 1, 1988
We present a comprehensive study of the axiom schemas 127 ", B27" (induction and collection schem... more We present a comprehensive study of the axiom schemas 127 ", B27" (induction and collection schemas for parameter free Z" formulas) and some closely related schemas. Introduction. This paper is divided into three main sections. In §1 we investigate the relationship between IZ~, BZ~ and their parameter counterparts ll", BZ". In §2 we prove a series of conservation results which enable us to give axiomatizations of the Z" + 2 and Z n+l consequences of IZ". Finally, in §3 we investigate the quantifier complexity and finite axiomatizability of these schemas. §0. Preliminaries and summary of main results. We work in the usual first-order language of arithmetic {0,1, +, •, <}. P" denotes a finite set of 77, axioms such that if M 1= P~, then M is the nonnegative part of a commutative discretely ordered ring (see [4] for a precise definition of P~). II~ is P~ together with the schema 0(0) A Vx(0(x)-• 0(x + 1))-»'Vx0(x), 0 e Z". BZ~ is P" + ir 0 together with the schema Vx3y0(x,y)-»• VzBtVx < z3y < td(x,y), 0 e S". LS~ is P" together with the schema 3x0(x)-> 3x(0(x) A Vy < x-i0(y)), 6 e I B .
Logica Universalis, Apr 18, 2022
On the basis of recent work concerning the meaning of the term stoicheion ( στοιχεῖον ) in Aristo... more On the basis of recent work concerning the meaning of the term stoicheion ( στοιχεῖον ) in Aristotle’s Analytics , we strengthen the view that this treatise can be viewed as a precursor of Euclid’s Elements .
Abstract. We give a negative solution to the first part of Problem 4 in [1], i.e. we show that EA... more Abstract. We give a negative solution to the first part of Problem 4 in [1], i.e. we show that EA (=Elementary Arithmetic) does not imply the parameter free induction schema for decidable predicates, I ∆ − 1. 1
Logica Universalis
On the basis of recent work concerning the meaning of the term stoicheion ( στοιχεῖον ) in Aristo... more On the basis of recent work concerning the meaning of the term stoicheion ( στοιχεῖον ) in Aristotle’s Analytics , we strengthen the view that this treatise can be viewed as a precursor of Euclid’s Elements .
Computability in Europe (CiE) is an informal network of European scientists working on computabil... more Computability in Europe (CiE) is an informal network of European scientists working on computability theory, including its foundations, technical development, and applications. Among the aims of the network is to advance our theoretical understanding of what can and cannot be computed, by any means of computation. Its scientific vision is broad: computations may be performed with discrete or continuous data by all kinds of algorithms, programs, and machines. Computations may be made by experimenting with any sort of physical system obeying the laws of a physical theory such as Newtonian mechanics, quantum theory, or relativity. Computations may be very general, depending on the foundations of set theory; or very specific, using the combinatorics of finite structures. CiE also works on subjects intimately related to computation, especially theories of data and information, and methods for formal reasoning about computations. The sources of new ideas and methods include practical deve...
The field of weak arithmetics is an application of logical methods to number theory that was deve... more The field of weak arithmetics is an application of logical methods to number theory that was developed by mathematicians, philosophers, and theoretical computer scientists. New Studies in Weak Arithmetics is dedicated to late Australian mathematician Alan Robert Woods (1953-2011), whose seminal thesis is published here for the first time. This volume also contains the unpublished but significant thesis of Hamid Lesan (1951-2006) as well as other original papers on topics addressed in Woods' thesis and life's work that were first presented at the 31st Journees sur les Arithmetiques Faibles meeting held in Samos, Greece, in 2012.
1. Thread algebra and risk assessment services Jan A. Bergstra, Inge Bethke and Alban Ponse 2. Co... more 1. Thread algebra and risk assessment services Jan A. Bergstra, Inge Bethke and Alban Ponse 2. Covering definable manifolds by open definable subsets Mario J. Edmundo 3. Isomorphisms and definable relations on computable models Sergei S. Goncharov 4. Independence for types in algebraically closed valued fields Deirdre Haskell 5. Simple groups of finite Morley rank Eric Jaligot 6. Towards a logic of type-free modality and truth Hannes Leitgeb 7. Structural analysis of Aronszajn trees Justin Tatch Moore 8. Proof analysis in non-classical logics Sara Negri 9. Paul Bernays' later philosophy of mathematics Charles Parsons 10. Proofnets for S5: sequents and circuits for modal logic Greg Restall 11. Recursion on the partial continuous functionals Helmut Schwichtenberg 12. A transactional approach to the logic of truth Michael Sheard 13. On some problems in computable topology Dieter Spreen 14. Monotone inductive definitions and consistency of New Foundations Sergei Tupailo.