Search results
Results from the WOW.Com Content Network
The decision problem for the existential theory of the reals is the algorithmic problem of testing whether a given sentence belongs to this theory; equivalently, for strings that pass the basic syntactical checks (they use the correct symbols with the correct syntax, and have no unquantified variables) it is the problem of testing whether the ...
For the interpretation of formulas, consider these structures: the positive real numbers, the real numbers, and complex numbers. The following example in first-order logic (=) is a sentence. This sentence means that for every y, there is an x such that =. This sentence is true for positive real numbers, false for real numbers, and true for ...
For example, if the domain is the set of all real numbers, one can assert in first-order logic the existence of an additive inverse of each real number by writing ∀x ∃y (x + y = 0) but one needs second-order logic to assert the least-upper-bound property for sets of real numbers, which states that every bounded, nonempty set of real numbers ...
In mathematical logic, an ω-consistent (or omega-consistent, also called numerically segregative) [1] theory is a theory (collection of sentences) that is not only (syntactically) consistent [2] (that is, does not prove a contradiction), but also avoids proving certain infinite combinations of sentences that are intuitively contradictory.
1. Add to Grains. Turn yesterday’s soup into today’s healthy bowl. Start with a base of grains like rice, farro, or quinoa. Add roasted veggies and a protein.
Russia said on Wednesday it had detained a man from Uzbekistan over the killing of a senior Russian general and his assistant in Moscow a day earlier. Lt. Gen. Igor Kirillov, who headed Russia’s ...
A Texas woman is charged with murder after police say she fatally shot her husband, lit his truck on fire and fled the scene in a kayak. Bexar County, Texas officials found the body of Tomas ...
A structure is said to model a set of first-order sentences in the given language if each sentence in is true in with respect to the interpretation of the signature previously specified for . (Again, not to be confused with the formal notion of an " interpretation " of one structure in another) A model of T {\displaystyle T} is a structure that ...