The Expressive Power of CSP Quantifiers

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• Lauri Hella, Tampere University
• Thursday 29 September 2022, 14:00-15:00
• SS03.

If you have a question about this talk, please contact Jamie Vicary.

A generalized quantifier Q is called a CSP -quantifier if its defining class consists of all structures that can be homomorphically mapped to a fixed finite template structure. For all positive integers n>1 and k, we define a pebble game that characterizes equivalence of structures with respect to the extension of the infinitary k-variable logic by all unary quantifiers and the class C_n of all CSP quantifiers with template structures that have at most n elements. Using these games we prove that for every n>1 there exists a CSP -quantifier with template of size n+1 which is not definable in finite variable logic with all unary quantifiers and quantifiers in C_n. The proof of this result is based on a new variation of the well-known Cai-Fürer-Immerman construction.

This talk is part of the Logic and Semantics Seminar (Computer Laboratory) series.

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