The key tool in proving inexpressibility results in finite-model theory is Ehrenfeucht-F'rai'ss6 games. This paper surveys various game-theoretic techniques and tools that lead to simpler proofs of inexpressibility results. The focus is on first-order logic and

In this paper we examine Ehrenfeucht-Fräıssé (EF) games on fields and vector spaces. We find the exact length of the EF game on two algebraically closed fields of finite transcendence degree over Q or Z/pZ. We also determine an upper bound on the length of any EF game on models (F1 ,F1) and (F m 2 ,F2 of vector spaces where m = n and a lower bound for the special case F1 = F2.

Assume 〈א0,א1〉 → 〈λ, λ +〉. Assume M is a model of a first order theory T of cardinality at most λ+ in a vocabulary L(T ) of cardinality ≤ λ. Let N be a model with the same vocabulary. Let ∆ be a set of first order formulas in L(T ) and let D be a regular filter on λ. Then M is ∆-embeddable into the reduced power N/D, provided that every ∆-existential formula true in M is true also in N . We obt...

Examples of effectively indiscernible projective sets real numbers in various models set theory are presented. We prove that it is true, Miller and Laver generic extensions the constructible universe, there exists a lightface ?21 equivalence relation on all nonconstructible reals, having exactly two classes, neither one which ordinal definable, therefore classes OD-indiscernible. A similar but ...

A model is said to be Leibnizian if it has no pair of indiscernibles. Mycielski has shown that there is a first order axiom LM (the LeibnizMycielski axiom) such that for any completion T of Zermelo-Fraenkel set theory ZF , T has a Leibnizian model iff T proves LM. Here we prove: Theorem A. Every complete theory T extending ZF + LM has 2 א 0 nonisomorphic countable Leibnizian models. Theorem B. ...

Abstract In his concept of a composer's creative work Mieczysław Tomaszewski distinguishes the late and final phases. Edward W. Said, on other hand, devoted last publication to reflections style in music literature, referring existing body research subject. What is position, context both these perspectives, three important works for voices instruments by Zygmunt Mycielski: Three Psalms , Liturg...