2 citations · 3 across the 3 of their papers we have counts for
4 papers
Decidability and classification of the theory of integers with primes
Itay Kaplan, Saharon Shelah
We show that under Dickson's conjecture about the distribution of primes in the natural numbers, the theory Th(Z,+,1,0,Pr) where Pr is a predicate for the prime numbers and their n…
Groups and fields with NTP2
Artem Chernikov, Itay Kaplan, Pierre Simon
NTP2 is a large class of first-order theories defined by Shelah and generalizing simple and NIP theories. Algebraic examples of NTP2 structures are given by ultra-products of p-adi…
Artin-Schreier extensions in NIP and simple fields
Itay Kaplan, Thomas Scanlon, Frank O. Wagner
We show that NIP fields have no Artin-Schreier extension, and that simple fields have only a finite number of them.
The automorphism tower of a centerless group (mostly) without choice
Itay Kaplan, Saharon Shelah
For a centerless group G, we can define its automorphism tower. We define G^{alpha} : G^0=G, G^{alpha +1}=Aut(G^alpha) and for limit ordinals G^delta=bigcup_{alpha < delta}G^alpha…