
The Pseudofinite Monadic Second Order Theory of Linear Order
Monadic second order logic is the expansion of first order logic by quan...
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Simulations and the Lamplighter group
We introduce a notion of "simulation" for labelled graphs, in which edge...
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Second Order Operators in the NASA Astrophysics Data System
Second Order Operators (SOOs) are database functions which form secondar...
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The firefighter problem on polynomial and intermediate growth groups
We prove that any Cayley graph G with degree d polynomial growth does no...
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The domino problem is undecidable on surface groups
We show that the domino problem is undecidable on orbit graphs of nonde...
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Monadic Second Order Logic with PathMeasure Quantifier is Undecidable
We prove that the theory of monadic second order logic (MSO) of the infi...
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Polymorphism and the obstinate circularity of second order logic: a victims' tale
The investigations on higherorder type theories and on the related noti...
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Monadic secondorder logic and the domino problem on selfsimilar graphs
We consider the domino problem on Schreier graphs of selfsimilar groups, and more generally their monadic secondorder logic. On the one hand, we prove that if the group is bounded then the graph's monadic secondorder logic is decidable. This covers, for example, the Sierpiński gasket graphs and the Schreier graphs of the Basilica group. On the other hand, we already prove undecidability of the domino problem for a class of selfsimilar groups, answering a question by Barbieri and Sablik, and some examples including one of linear growth.
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