Logic, Sets and Numbers 1

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Across
  1. 2. Gives name to the postulates of the natural numbers
  2. 3. Characteristic property of the rationals Q in R
  3. 5. First ordinal number in each class
  4. 7. Gives name, together with Forti, to a well-known paradox
  5. 10. Law that establishes that for any pair of cardinal numbers a,b, one of the following holds: a>b, a=b, a<b
  6. 13. Third of the headings required for the construction of real numbers, other than the axioms of order and arithmetic
  7. 16. Completed Gödel's argumentation to prove that the continuum hypothesis is independent of the axioms of formal set theory
  8. 18. A real number that is not algebraic
  9. 19. Lemma asserting the existence of at least one maximal element in a partially ordered set whose partially ordered subsets admit an upper bound
  10. 20. Said of a real number obtainable by elementary arithmetic operations and extraction of n^th roots
Down
  1. 1. Said of an homomorphism f:(A,I) of a monadic logic into a model (B,{0}) with f(I)=0
  2. 4. Any Dedekind section determines a
  3. 6. Property of distinct equivalence classes
  4. 8. Author of "Theory of Sets and Transfinite Arithmetic"
  5. 9. Order in which the totality condition is replaced by reflexivity
  6. 11. A proposition P(p,q,...) such that P(a,b,...) holds for any statements a,b,...
  7. 12. Theorem characterizing first-order logic
  8. 14. Said of a prime number p such that p+2 is also prime
  9. 15. Boolean algebra with an existence quantifier
  10. 17. Besides the axiom of choice, the second further axiom required by the Zermelo-Fraenkel theory