Temat: complete representations - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: On Complete Representations and Minimal Completions in Algebraic Logic, Both Positive and Negative Results
Autorzy:: Sayed Ahmed, Tarek
Powiązania:: https://bibliotekanauki.pl/articles/2033851.pdf
Data publikacji:: 2021-07-21
Wydawca:: Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:: Algebraic logic
relation algebras
cylindric algebras
polyadic algebras
complete representations
Opis:: 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 $\mathbf{PA}_{\alpha}(\mathsf{PEA}_{\alpha})$ stand for the class of polyadic (equality) algebras of dimension $\alpha$. We reprove that the class $\mathsf{CRCA}_n$ of completely representable $\mathsf{CA}_n$s, and the class $\sf CRRA$ of completely representable $\mathsf{RA}$s are not elementary, a result of Hirsch and Hodkinson. We extend this result to any variety $\sf V$ between polyadic algebras of dimension $n$ and diagonal free $\mathsf{CA}_n$s. We show that that the class of completely and strongly representable algebras in $\sf V$ is not elementary either, reproving a result of Bulian and Hodkinson. For relation algebras, we can and will, go further. We show the class $\sf CRRA$ is not closed under $\equiv_{\infty,\omega}$. In contrast, we show that given $\alpha\geq \omega$, and an atomic $\mathfrak{A}\in \mathsf{PEA}_{\alpha}$, then for any $n<\omega$, $\mathfrak{Nr}_n\mathfrak{A}$ is a completely representable $\mathsf{PEA}_n$. We show that for any $\alpha\geq \omega$, the class of completely representable algebras in certain reducts of $\mathsf{PA}_{\alpha}$s, that happen to be varieties, is elementary. We show that for $\alpha\geq \omega$, the the class of polyadic-cylindric algebras dimension $\alpha$, introduced by Ferenczi, the completely representable algebras (slightly altering representing algebras) coincide with the atomic ones. In the last algebras cylindrifications commute only one way, in a sense weaker than full fledged commutativity of cylindrifications enjoyed by classical cylindric and polyadic algebras. Finally, we address closure under Dedekind-MacNeille completions for cylindric-like algebras of dimension $n$ and $\mathsf{PA}_{\alpha}$s for $\alpha$ an infinite ordinal, proving negative results for the first and positive ones for the second.
Źródło:: Bulletin of the Section of Logic; 2021, 50, 4; 465-511
0138-0680
2449-836X
Pojawia się w:: Bulletin of the Section of Logic
Dostawca treści:: Biblioteka Nauki

Artykuł

Zmień widok

na półce

Skocz do pozycji: 2.

Tytuł:: A new division formula for complete intersections
Autorzy:: Passare, Mikael
Powiązania:: https://bibliotekanauki.pl/articles/1312650.pdf
Data publikacji:: 1991
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: complete intersections
residue currents
integral representations
Opis:: We provide a new division formula for holomorphic mappings. It is given in terms of residue currents and has the advantage of being more explicit and simpler to prove than the previously known formulas.
Źródło:: Annales Polonici Mathematici; 1991, 55, 1; 283-286
0066-2216
Pojawia się w:: Annales Polonici Mathematici
Dostawca treści:: Biblioteka Nauki

Artykuł

Zmień widok

na półce

Skocz do pozycji: 3.

Tytuł:: Around Widders characterization of the Laplace transform of an element of $L^{∞}(ℝ^{+})$
Autorzy:: Kisyński, Jan
Powiązania:: https://bibliotekanauki.pl/articles/1207972.pdf
Data publikacji:: 2000
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: operators from $L_{ϰ}^{1}(ℝ^{+})$ into a Banach space
complete monotonicity and positivity with respect to a cone
one-parameter semigroups of operators
vector measures
Gelfand space
Radon-Nikodym property
representations of the convolution algebra $L_{ϰ}^{1}(ℝ^{+})$
pseudoresolvents and their generators
real inversion formulas for the Laplace transform
Opis:: Let ϰ be a positive, continuous, submultiplicative function on $ℝ^{+}$ such that $lim_{t→∞} e^{-ωt}t^{-α}ϰ(t) = a$ for some ω ∈ ℝ, α ∈ $\overline{ℝ^{+}}$ and $a ∈ ℝ^{+}$. For every λ ∈ (ω,∞) let $ϕ_{λ}(t) =e^{-λt}$ for $t ∈ ℝ^{+}$. Let $L^{1}_{ϰ}(ℝ^{+})$ be the space of functions Lebesgue integrable on $ℝ^{+}$ with weight $ϰ$, and let E be a Banach space. Consider the map $ϕ_{•}: (ω,∞) ∋ λ → ϕ_{λ} ∈ L_{ϰ}^{1}(ℝ^{+})$. Theorem 5.1 of the present paper characterizes the range of the linear map $T → Tϕ_{•}$ defined on $L(L_{ϰ}^{1}(ℝ^{+});E)$, generalizing a result established by B. Hennig and F. Neubrander for $ϰ(t)=e^{ωt}$. If ϰ ≡ 1 and E =ℝ then Theorem 5.1 reduces to D. V. Widder's characterization of the Laplace transform of a function in $L^{∞}(ℝ^{+})$. Some applications of Theorem 5.1 to the theory of one-parameter semigroups of operators are discussed. In particular a version of the Hille-Yosida generation theorem is deduced for $C_0$ semigroups $(S_t)_{t ∈ \overline{ℝ^{+}}}$ such that $sup_{t ∈ \overline{ℝ^{+}}} (ϰ(t))^{-1}∥ S_t∥ < ∞$.
Źródło:: Annales Polonici Mathematici; 2000, 74, 1; 161-200
0066-2216
Pojawia się w:: Annales Polonici Mathematici
Dostawca treści:: Biblioteka Nauki

Artykuł

Zmień widok

na półce

Informacja

Wyszukujesz frazę "complete representations" wg kryterium: Temat

Źródło danych

Dostawca treści

Kolekcja

Rok wydania

Wydawca

Temat

Autor

Typ dokumentu

Język