Moreover, Gödel’s second incompleteness theorem shows that the consistency of sufficiently strong recursively enumerable theories of arithmetic can be tested in a particular way. A theory is complete if, for every formula φ in its language, at least one of φ or ¬φ is a logical consequence of the theory. Hilbert’s program was strongly impacted by the incompleteness theorems, which showed that sufficiently strong proof theories cannot prove their consistency (provided that they are consistent). The early development of mathematical proof theory was driven by the desire to provide finitary consistency proofs for all of mathematics as part of Hilbert’s program. In a sound formal system, every satisfiable theory is consistent, but the converse does not hold.
To add consistent to a word list please sign up or log in. To add consistency to a word list please sign up or log in. These set theories cannot prove their own Gödel sentence—provided that they are consistent, which is generally believed. Such a theory is consistent if and only if it does not prove a particular sentence, called the Gödel sentence of the theory, which is a formalized statement of the claim that the theory is indeed consistent.
consistent American Dictionary
Clear and consistent communication is essential for team collaboration.23. Financial consistency is crucial for long-term financial planning.21. The writer’s consistency in delivering thought-provoking content is commendable.20. Maintaining consistency in daily routines can lead to a more organized life.19.
The artist’s consistency in producing high-quality artwork gained them a loyal following.5. A well-written document should have consistency in style, grammar, and formatting.4. The athlete’s consistent training regimen contributed to their exceptional performance in the competition.3. The teacher recognized the student’s consistent effort and improvement in their academic performance. A strong team is built on the consistency of communication and collaboration.6. The chef’s culinary creations are praised for their consistency in flavor and presentation.5.
A theory is satisfiable if it has a model, i.e., there exists an interpretation under which all axioms in the theory are true. Definition of consistent adjective from the Oxford Advanced American Dictionary Definition of consistency noun from the Oxford Advanced American Dictionary Definition of consistent adjective from the Oxford Advanced Learner’s Dictionary
The consistency of his behavior in difficult situations earned him respect.18. Achieving consistency in flavor is the goal of any seasoned cook.16. The athlete’s remarkable consistency in winning races is a testament to their skill.14. The consistency of her dedication to the cause is truly inspiring.13. Building a brand requires maintaining consistency in messaging and visuals.12.
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This is what consistent meant in traditional Aristotelian logic, although in contemporary mathematical logic the term satisfiable is used instead. A trivial theory (i.e., one which proves every sentence in the language of the theory) is clearly inconsistent. Much like resetting a thermostat – over time, slow, consistent adjustments can help the body accept a new, healthier range. First recorded in 1565–75, consistent is from the Latin word consistent- (stem of consistēns, present participle of consistere ); consist, -ent The term ‘consistency’ maintains its etymological connection to the concept of standing together, emphasizing the idea of reliability and stability in various contexts. French-English dictionary, translator, and learning
consistent
Spanish-English dictionary, translator, and learning English dictionary and learning for Spanish speakers These are words often used in combination with consistency. Gödel’s theorem applies to the theories of Peano arithmetic (PA) and primitive recursive arithmetic (PRA), but not to Presburger arithmetic.
All content on this website, including dictionary, thesaurus, literature, geography, and other reference data is for informational purposes only. Over 500,000 expert-authored dictionary and thesaurus entries Definitions and idiom definitions from Dictionary.com Unabridged, based on the Random House Unabridged Dictionary, © Random House, Inc. 2023 The players and staff, how we are doing this season, how we are feeling, how we needed to keep the same consistency as before. “It also gives pets like Fern the calm, consistency and connection they simply can’t get in a kennel environment.”
Derived terms
- These set theories cannot prove their own Gödel sentence—provided that they are consistent, which is generally believed.
- Clear and consistent communication is essential for team collaboration.23.
- To add consistent to a word list please sign up or log in.
- Definition of consistency noun from the Oxford Advanced Learner’s Dictionary
- The consistency of her performance throughout the project was admirable.7.
- In theories of arithmetic, such as Peano arithmetic, there is an intricate relationship between the consistency of the theory and its completeness.
Gödel’s incompleteness theorems show that any sufficiently strong recursively enumerable theory of arithmetic cannot be both complete and consistent. In theories of arithmetic, such as Peano arithmetic, there is an intricate relationship between the consistency of the theory and its completeness. Although consistency can be proved using model theory, it is often done in a purely syntactical way, without any need to reference some model of the logic. A consistency proof is a mathematical proof that a particular theory is consistent. In deductive logic, a consistent theory is one that does not lead to a logical contradiction.
- English dictionary and learning for Spanish speakers
- Product consistency is essential to meet customer expectations.10.
- Achieving consistency in flavor is the goal of any seasoned cook.16.
- The success of a diet plan relies on the consistency of healthy eating habits.6.
- A trivial theory (i.e., one which proves every sentence in the language of the theory) is clearly inconsistent.
- The same result is true for recursively enumerable theories that can describe a strong enough fragment of arithmetic—including set theories such as Zermelo–Fraenkel set theory (ZF).
Maintaining consistency in your exercise routine will yield better results over time.4. The success of a business relies on the consistency of its product or service quality.3. In order to improve your skills, practice with consistency is key.2. It involves a commitment to maintaining the same level of quality, accuracy, or effort consistently, regardless of external circumstances or challenges. Uniformity, inconsistency, variability, fluctuation
Definitions for Consistencykənˈsɪs tən sicon·sis·ten·cy
But the problem for Rubin is that, as he noted in November, there is no longer the consistent buying that has been present for the past several months. But even as doctors see a path to eliminate this type of cancer, they have battled with limited access to early, consistent screening and care. In sports, achieving and maintaining consistency is the key to sustained success. The athlete’s unwavering consistency in performance was unmatched.24.
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“He will crave greatness and real consistency. He will fine-tune that balance.” What’s so unique about where Equinox stands against that backdrop is that what’s real is about hard work, the consistency, the discipline that’s required to show up and fuel that transformation. Examples are provided to illustrate real-world usage of words in context. Definition of consistency noun from the Oxford Advanced consistency meaning Learner’s Dictionary
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The team’s consistency in meeting deadlines impressed their clients.11. Product consistency is essential to meet customer expectations.10. The chef’s success is attributed to the unwavering consistency of his dishes.9. The consistency of her performance throughout the project was admirable.7. The success of a diet plan relies on the consistency of healthy eating habits.6.