query: Why does a definition of multiplication in Presburger Arithmetic result in an undecidable theory?
positive_passages.docid: 149976
positive_passages.text: What is "magic" about the combination of addition and multiplication in formal arithmetic?
negative_passages.docid: 10606
negative_passages.text: Finding how multiplication and addition behave on $\mathbb{F}_4$ without any result
negative_passages.docid: 14121
negative_passages.text: What is the logic behind uncountable nouns?
negative_passages.docid: 64545
negative_passages.text: Continuum between addition, multiplication and exponentiation?
negative_passages.docid: 2269
negative_passages.text: Proof that the real numbers are countable: Help with why this is wrong
negative_passages.docid: 14849
negative_passages.text: Decidability of a predicate.
negative_passages.docid: 53399
negative_passages.text: Proof of the uncountability of reals using the diagonal argument—problem?
negative_passages.docid: 76809
negative_passages.text: "Some" and "Any"; countables and uncountable
negative_passages.docid: 4769
negative_passages.text: Any reasons why the basis case can't be at the end of a mathematical induction proof?
negative_passages.docid: 78290
negative_passages.text: Countable axiom of choice: why you can't prove it from just ZF
negative_passages.docid: 5893
negative_passages.text: On the commutative property of multiplication (domain of integers, possibly reals)
negative_passages.docid: 46430
negative_passages.text: A simple decision problem whose decidability is not known
negative_passages.docid: 83116
negative_passages.text: Uncountability of basis of $\mathbb R^{\mathbb N}$
negative_passages.docid: 5035
negative_passages.text: Can unprovability unprovable? Is there an $\omega$-fold unprovability?
negative_passages.docid: 108748
negative_passages.text: Why there are real numbers with infinite digits, but no such natural numbers (or another reason why real numbers are uncountable)
negative_passages.docid: 155777
negative_passages.text: Show that infinite Cartesian product is uncountable
negative_passages.docid: 18160
negative_passages.text: How to show that the group of nonzero real numbers under multiplication is not isomorphic to the group of real numbers under addition?