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WikiCards · Card list · Science cards · Gödel's completeness theorem
Uncommon card · Science
Gödel's completeness theorem, an Uncommon card
Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic.
- Rarity
- Uncommon
- Domain
- Science
- ATK
- 63
- DEF
- 33
- Power
- 96
- Wikipedia reads a year
- 49,000
Power 96 (ATK + DEF): stronger than 40 % of WikiCards cards.
Gödel's completeness theorem quiz: 3 questions
Three questions on the Gödel's completeness theorem card, the way WikiCards duels ask them. Pick an answer, the facts are just below.
Find the missing word
One ______ says this as "anything true in all models is provable".
Answer
sometimes. One sometimes says this as "anything true in all models is provable". From the Gödel's completeness theorem article on Wikipedia.
Which of these cards hits hardest (highest ATK)?
Answer
Gödel's completeness theorem. Gödel's completeness theorem 63 · Laziness 60 · BMW 1 Series 56 · Araku Valley 53 ATK in WikiCards.
In a duel, each round asks a question like these about the opposing card, with 15 seconds to answer.
The facts on the card
The card carries these facts from its Wikipedia article.
- The completeness theorem applies to any first-order theory: If T is such a theory, and φ is a sentence and every model of T is a model of φ, then there is a proof of φ using the statements of T as axioms.
- One sometimes says this as "anything true in all models is provable".
- The completeness theorem makes a close link between model theory, which deals with what is true in different models, and proof theory, which studies what can be formally proven in particular formal systems.
Why it is Uncommon
Rarity in WikiCards follows a year of Wikipedia page views: the most read articles become Epic and Legendary cards. The Gödel's completeness theorem article was read about 49,000 times in a year. ATK comes from the length of the article and DEF from its quality, so this card hits with 63 and blocks with 33: each hit it takes is cut by 13 %.
How to get Gödel's completeness theorem
Open packs. Each pack holds five cards drawn from real Wikipedia articles, the rarest last, and the fifth card is always Rare or better. The odds are shown in the game. A free pack arrives every hour and two can wait, and the Coins you win in duels buy more packs.
More Science cards
Cards close in power
The cards just above and just below Gödel's completeness theorem in the power ranking, all domains together.
- Araku ValleyUncommon · Nature · ATK 53 DEF 43
- ConvolvulaceaeUncommon · Nature · ATK 62 DEF 34
- Fakhruddin AhmedUncommon · Science · ATK 57 DEF 39
- LazinessUncommon · Science · ATK 60 DEF 36
- Pope LiberiusUncommon · History · ATK 56 DEF 40
- ResortUncommon · Arts · ATK 56 DEF 40
Card lists
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Credits
Text : Wikipedia, Gödel's completeness theorem (revision), CC BY-SA 4.0. Photo : Fschwarzentruber, CC BY-SA 4.0, Wikimedia Commons.
