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Complete Representations and Neat Embeddings
(Wydawnictwo Uniwersytetu Łódzkiego, 2022-09-09)
Let \(2<n<\omega\). Then \({\sf CA}_n\) denotes the class of cylindric algebras of dimension \(n\), \({\sf RCA}_n\) denotes the class of representable \(\sf CA_n\)s, \({\sf CRCA}_n\) denotes the class of completely ...
On Complete Representations and Minimal Completions in Algebraic Logic, Both Positive and Negative Results
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-07-21)
Fix a finite ordinal \(n\geq 3\) and let \(\alpha\) be an arbitrary ordinal. Let \(\mathsf{CA}_n\) denote the class of cylindric algebras of dimension \(n\) and \(\sf RA\) denote the class of relation algebras. Let ...
Omitting Types in Fragments and Extensions of First Order Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-05-28)
Fix \(2 < n < \omega\). Let \(L_n\) denote first order logic restricted to the first n variables. Using the machinery of algebraic logic, positive and negative results on omitting types are obtained for \(L_n\) and for ...
Lifting Results for Finite Dimensions to the Transfinite in Systems of Varieties Using Ultraproducts
(Wydawnictwo Uniwersytetu Łódzkiego, 2024-02-12)
We redefine a system of varieties definable by a schema of equations to include finite dimensions. Then we present a technique using ultraproducts enabling one to lift results proved for every finite dimension to the ...