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- Saharon Shelah
- 1993

Gurevich and Shelah have shown that Peano Arithmetic cannot be interpreted in the monadic second-order theory of short chains (hence, in the monadic secondorder theory of the real line). We will show here that it is consistent that there is no interpretation even in the monadic second-order theory of all chains.

- Yuri Gurevich, Saharon Shelah
- 26th Annual Symposium on Foundations of Computer…
- 1985

We prove that the three extensions of first-order logic by means of positive inductions, monotone inductions, and so-called non-monotone (in our terminology, inflationary) inductions respectively, all have the same expressive power in the case of finite structures. As a by-product, the collapse of the corresponding fixed-point hierarchies can be deduced.

The formalism of temporal Logic has been suggested as a most appropriate tool, for reasoning about programs and their Originally, temporal Logic has been designed in order to analyze and reason about time sequences in general. Formalizing the possible variations in time of a varying (dynamic) situation, we consider time sequences s0, s1, . . . , where each… (More)

- Menachem Magidor, Saharon Shelah
- Arch. Math. Log.
- 1996

Assuming some large cardinals, a model of ZFC is obtained in which אω+1 carries no Aronszajn trees. It is also shown that if λ is a singular limit of strongly compact cardinals, then λ carries no Aronszajn trees.

- Menachem Kojman, Saharon Shelah
- J. Symb. Log.
- 1992

Our theme is that not every interesting question in set theory is independent of ZFC. We give an example of a rst order theory T with countable D(T) which cannot have a universal model at @ 1 without CH; we prove in ZFC a covering theorem from the hypothesis of the existence of a universal model for some theory; and we prove | again in ZFC | that for a… (More)

- Saharon Shelah
- 2002

Motivated by the minimal tower problem, an earlier work studied diagonalizations of covers where the covers are related to linear quasiorders (τ -covers). We deal with two types of combinatorial questions which arise from this study. 1. Two new cardinals introduced in the topological study are expressed in terms of well known cardinals characteristics of… (More)

- Andreas Blass, Yuri Gurevich, Saharon Shelah
- Ann. Pure Appl. Logic
- 1999

Turing machines define polynomial time (PTime) on strings but cannot deal with structures like graphs directly, and there is no known, easily computable string encoding of isomorphism classes of structures. Is there a computation model whose machines do not distinguish between isomorphic structures and compute exactly PTime properties? This question can be… (More)

- Uri Abraham, Matatyahu Rubin, Saharon Shelah
- Ann. Pure Appl. Logic
- 1985

We apply model theoretic methods to the problem of existence of countable universal graphs with finitely many forbidden connected subgraphs. We show that to a large extent the question reduces to one of local finiteness of an associated “algebraic closure” operator (Theorem 3, §3). The main applications are new examples of universal graphs with forbidden… (More)