Joel David - Profile on Academia.edu (original) (raw)

Papers by Joel David

Annals of Pure and Applied Logic, 2000

The lottery preparation, a new general kind of Laver preparation, works uniformly with supercompa... more The lottery preparation, a new general kind of Laver preparation, works uniformly with supercompact cardinals, strongly compact cardinals, strong cardinals, measurable cardinals, or what have you. And like the Laver preparation, the lottery preparation makes these cardinals indestructible by various kinds of further forcing. A supercompact cardinal κ, for example, becomes fully indestructible by <κ-directed closed forcing; a strong cardinal κ becomes indestructible by ≤κ-strategically closed forcing; and a strongly compact cardinal κ becomes indestructible by, among others, the forcing to add a Cohen subset to κ, the forcing to shoot a club C ⊆ κ avoiding the measurable cardinals and the forcing to add various long Prikry sequences. The lottery preparation works best when performed after fast function forcing, which adds a new completely general kind of Laver function for any large cardinal, thereby freeing the Laver function concept from the supercompact cardinal context.

Physical Review Letters, 1993

We use the zero-temperature random-field Ising model to study hysteretic behavior at first-order ... more We use the zero-temperature random-field Ising model to study hysteretic behavior at first-order phase transitions. Sweeping the external field through zero, the model exhibits hysteresis, the return-point memory effect, and avalanche fluctuations. There is a critical value of disorder at which a jump in the magnetization (corresponding to an infinite avalanche) first occurs. We study the universal behavior at this critical point using mean-field theory, and also present preliminary results of numerical simulations in three dimensions.

Annals of Pure and Applied Logic, 2000

The lottery preparation, a new general kind of Laver preparation, works uniformly with supercompa... more The lottery preparation, a new general kind of Laver preparation, works uniformly with supercompact cardinals, strongly compact cardinals, strong cardinals, measurable cardinals, or what have you. And like the Laver preparation, the lottery preparation makes these cardinals indestructible by various kinds of further forcing. A supercompact cardinal κ, for example, becomes fully indestructible by <κ-directed closed forcing; a strong cardinal κ becomes indestructible by ≤κ-strategically closed forcing; and a strongly compact cardinal κ becomes indestructible by, among others, the forcing to add a Cohen subset to κ, the forcing to shoot a club C ⊆ κ avoiding the measurable cardinals and the forcing to add various long Prikry sequences. The lottery preparation works best when performed after fast function forcing, which adds a new completely general kind of Laver function for any large cardinal, thereby freeing the Laver function concept from the supercompact cardinal context.

Physical Review Letters, 1993

We use the zero-temperature random-field Ising model to study hysteretic behavior at first-order ... more We use the zero-temperature random-field Ising model to study hysteretic behavior at first-order phase transitions. Sweeping the external field through zero, the model exhibits hysteresis, the return-point memory effect, and avalanche fluctuations. There is a critical value of disorder at which a jump in the magnetization (corresponding to an infinite avalanche) first occurs. We study the universal behavior at this critical point using mean-field theory, and also present preliminary results of numerical simulations in three dimensions.