finitely axiomatizable quasivariety (english) - meaning, definition, translation, pronunciation

Part of Speech

Noun Phrase

Phonetic Transcription

/fɪˈnaɪtli ˌæksɪˈmætɪzaɪzəbl ˌkwɑːzɪˈværɪti/

Meaning and Usage

A "finitely axiomatizable quasivariety" is a specific term used in the field of mathematical logic and algebra.

• Finitely Axiomatizable: Refers to a property of a structure that can be completely described by a finite set of axioms.
• Quasivariety: A generalization of a variety in universal algebra. While a variety is defined by equational properties, a quasivariety is defined by quasi-identifiable properties, which may include additional structures or conditions.

This term is predominantly used in academic and specialized contexts within mathematics and theoretical computer science. Its frequency of use is moderate, primarily found in written texts, such as journal articles, textbooks, and conference papers.

Example Sentences

1. "In certain algebraic frameworks, we can prove that a finitely axiomatizable quasivariety exists for specific classes of algebras."

2. "В некоторых алгебраических структурах мы можем доказать, что существует конечная аксиоматизируемая квазивариантность для конкретных классов алгебр."

3. "The study of finitely axiomatizable quasivarieties has significant implications for the categorization of algebraic systems."

4. "Изучение конечных аксиоматизируемых квазивариантов имеет важные последствия для категоризации алгебраических систем."

5. "Researchers are investigating the properties of finitely axiomatizable quasivarieties to better understand their applicability in model theory."

6. "Исследователи изучают свойства конечных аксиоматизируемых квазиварий, чтобы лучше понять их применимость в теории моделей."

Idiomatic Expressions

While the phrase "finitely axiomatizable quasivariety" is not part of common idiomatic expressions, discussing related concepts in the field can involve several important phrases:

1. "Quasivarieties of varying types are regularly compared to analyze their axiomatizability."

2. "Квазиварианты различных типов регулярно сравниваются для анализа их аксиоматизируемости."

3. "The concept of finitely axiomatizable structures leads to deeper insights in algebraic logic."

4. "Концепция конечных аксиоматизируемых структур приводит к более глубоким пониманиям в алгебраической логике."

5. "In geometry, our understanding of quasivarieties helps to unify different geometrical principles."

6. "В геометрии наше понимание квазиварий помогает объединить различные геометрические принципы."

Etymology

The term "finitely axiomatizable" combines "finite," derived from Latin "finitus," meaning "limited," with "axiomatizable," which is derived from the word "axiom" (from Greek "axiōma," meaning "that which is deemed worthy"). The term "quasivariety" originates from the word "variety," which in this context refers to a class of algebraic structures defined by identities, introduced in abstract algebra, paired with the prefix "quasi-" from Latin meaning "as if" to denote its generalized nature.

Synonyms and Antonyms

Synonyms: - Finite axiomatic system - Finite axiomatic framework - Restricted quasivariety

Antonyms: - Infinitely axiomatizable structure - Non-axiomatizable class - Broad quasivariety

This response provides a comprehensive overview of the term "finitely axiomatizable quasivariety," detailing its meaning, usage, and related linguistic features in the context of mathematics and logic.