Works by Fred G. Abramson

4 found
Order:
1. Models without indiscernibles.Fred G. Abramson & Leo A. Harrington - 1978 - Journal of Symbolic Logic 43 (3):572-600.
For T any completion of Peano Arithmetic and for n any positive integer, there is a model of T of size $\beth_n$ with no (n + 1)-length sequence of indiscernibles. Hence the Hanf number for omitting types over T, H(T), is at least $\beth_\omega$ . (Now, using an upper bound previously obtained by Julia Knight H (true arithmetic) is exactly $\beth_\omega$ ). If T ≠ true arithmetic, then $H(T) = \beth_{\omega1}$ . If $\delta \not\rightarrow (\rho)^{ , then any completion of (...) Direct download (6 more) Export citation Bookmark 11 citations 2. Models and Types of Peano's Arithmetic.Haim Gaifman, Julia F. Knight, Fred G. Abramson & Leo A. Harrington - 1983 - Journal of Symbolic Logic 48 (2):484-485. Direct download Export citation Bookmark 5 citations 3. Σ1-separation.Fred G. Abramson - 1979 - Journal of Symbolic Logic 44 (3):374 - 382. Let A be a standard transitive admissible set. Σ 1 -separation is the principle that whenever X and Y are disjoint Σ A 1 subsets of A then there is a Δ A 1 subset S of A such that$X \subseteq S$and$Y \cap S = \varnothing$. Theorem. If A satisfies Σ 1 -separation, then (1) If$\langle T_n\mid n is a sequence of trees on ω each of which has at most finitely many infinite paths in (...)
Let α be any countable admissible ordinal greater than ω. There is a transitive set A such that A is admissible, locally countable, On A = α, and A satisfies Σ 1 -separation. In fact, if B is any nonstandard model of $KP + \forall x \subseteq \omega$ (the hyperjump of x exists), the ordinal standard part of B is greater than ω, and every standard ordinal in B is countable in B, then HC B ∩ (standard part of B) (...)