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SUMMARY:The Expressive Power of CSP Quantifiers - Lauri Hella\, Tampere Un
 iversity
DTSTART:20220929T130000Z
DTEND:20220929T140000Z
UID:TALK178169@talks.cam.ac.uk
CONTACT:Jamie Vicary
DESCRIPTION:A generalized quantifier Q is called a CSP-quantifier if its d
 efining\nclass consists of all structures that can be homomorphically mapp
 ed to a\nfixed finite template structure. For all positive integers n>1 an
 d k\, we\ndefine a pebble game that characterizes equivalence of structure
 s with\nrespect to the extension of the infinitary k-variable logic by all
  unary\nquantifiers and the class C_n of all CSP quantifiers with template
 \nstructures that have at most n elements. Using these games we prove that
 \nfor every n>1 there exists a CSP-quantifier with template of size n+1\nw
 hich is not definable in finite variable logic with all unary\nquantifiers
  and quantifiers in C_n. The proof of this result is based on\na new varia
 tion of the well-known Cai-Fürer-Immerman construction.
LOCATION:SS03
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