Carreiro, Facundo and Facchini, Alessandro and Venema, Yde and Zanasi, Fabio
(2022)
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Model theory of monadic predicate logic with the infinity quantifier.
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*Archive for Mathematical Logic*, 61 (3-4).
pp. 465-502.

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## Abstract

This paper establishes model-theoretic properties of , a variation of monadic first-order logic that features the generalised quantifier ‘there are infinitely many’. We will also prove analogous versions of these results in the simpler setting of monadic first-order logic with and without equality. For each logic we will show the following. We provide syntactically defined fragments characterising four different semantic properties of sentences: (1) being monotone and (2) (Scott) continuous in a given set of monadic predicates; (3) having truth preserved under taking submodels or (4) being truth invariant under taking quotients. In each case, we produce an effectively defined map that translates an arbitrary sentence S to a sentence S' belonging to the corresponding syntactic fragment, with the property that S is equivalent to S' precisely when it has the associated semantic property. As a corollary of our developments, we obtain that the four semantic properties above are decidable for sentences.

Item Type: | Scientific journal article, Newspaper article or Magazine article |
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Subjects: | Mathematical sciences |

Department/unit: | Dipartimento tecnologie innovative > Istituto Dalle Molle di studi sull’intelligenza artificiale USI-SUPSI |

Depositing User: | Alessandro Facchini |

Date Deposited: | 24 Aug 2023 13:30 |

Last Modified: | 24 Aug 2023 13:30 |

URI: | http://repository.supsi.ch/id/eprint/14552 |

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