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On two-variable guarded fragment logic with expressive local Presburger constraints

Chia-Hsuan Lu ; Tony Tan.

We consider the extension of the two-variable guarded fragment logic with local Presburger quantifiers. These are quantifiers that can express properties such as "the number of incoming blue edges plus twice the number of outgoing red edges is at most three times the number of incoming green edges"&nbsp;[&hellip;]

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A note on first-order spectra with binary relations

Eryk Kopczynski ; Tony Tan.

The spectrum of a first-order sentence is the set of the cardinalities of its finite models. In this paper, we consider the spectra of sentences over binary relations that use at least three variables. We show that for every such sentence $\Phi$, there is a sentence $\Phi'$ that uses the same number&nbsp;[&hellip;]

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