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strictly weaker

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  • Boolean prime ideal theorem — In mathematics, a prime ideal theorem guarantees the existence of certain types of subsets in a given abstract algebra. A common example is the Boolean prime ideal theorem, which states that ideals in a Boolean algebra can be extended to prime… …   Wikipedia

  • Reverse mathematics — is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. The method can briefly be described as going backwards from the theorems to the axioms. This contrasts with the ordinary… …   Wikipedia

  • Axiom of countable choice — The axiom of countable choice or axiom of denumerable choice, denoted ACω, is an axiom of set theory, similar to the axiom of choice. It states that any countable collection of non empty sets must have a choice function. Spelled out, this means… …   Wikipedia

  • Dedekind-infinite set — In mathematics, a set A is Dedekind infinite if some proper subset B of A is equinumerous to A. Explicitly, this means that there is a bijective function from A onto some proper subset B of A. A set is Dedekind finite if it is not Dedekind… …   Wikipedia

  • Continuous function — Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables Implicit differentiation Taylor s theorem Related rates …   Wikipedia

  • Pebble automaton — A pebble automaton is an extension of tree walking automata which allows the automaton to use a finite amount of pebbles , used for marking tree node. The result is a model stronger than ordinary tree walking automata, but still strictly weaker… …   Wikipedia

  • ω-automaton — In automata theory, a branch of theoretical computer science, an ω automaton (or stream automaton) is a deterministic or nondeterministic automaton that runs on infinite, rather than finite, strings as input. Since ω automata do not stop, they… …   Wikipedia

  • Ideal (order theory) — In mathematical order theory, an ideal is a special subset of a partially ordered set (poset). Although this term historically was derived from the notion of a ring ideal of abstract algebra, it has subsequently been generalized to a different… …   Wikipedia

  • Hahn–Banach theorem — In mathematics, the Hahn–Banach theorem is a central tool in functional analysis. It allows the extension of bounded linear operators defined on a subspace of some vector space to the whole space, and it also shows that there are enough… …   Wikipedia

  • Order-embedding — In mathematical order theory, an order embedding is a special kind of monotone function, which provides a way to include one partially ordered set into another. Like Galois connections, order embeddings constitute a notion which is strictly… …   Wikipedia

  • Abstract rewriting system — In mathematical logic and theoretical computer science, an abstract rewriting system (also (abstract) reduction system or abstract rewrite system; abbreviation ARS) is a formalism that captures the quintessential notion and properties of… …   Wikipedia

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