The pair (ℵ_n,ℵ₀) may fail ℵ₀--compactness

2004/04/13 by Saharon Shelah, Shelah, Saharon
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Rings, Modules, and Algebras #math.LO

paper · pdf · doi:10.48550/arxiv.math/0404240

published as in: {Logic Colloquium '01} (2005) 402--433

arxiv created 2004/04/13 · arxiv updated 2009/12/01

Abstract

Let P be a distinguished unary predicate and K= M: M a model of cardinality aleph_n with P^M of cardinality aleph₀. We prove that consistently for n=4, for some countable first order theory T we have: T has no model in K whereas every finite subset of T has a model in K. We then show how we prove it also for n=2, too.

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