منابع مشابه
Division by zero in non-involutive meadows
Meadows have been proposed as alternatives for fields with a purely equational axiomatization. At the basis of meadows lies the decision to make the multiplicative inverse operation total by imposing that the multiplicative inverse of zero is zero. Thus, the multiplicative inverse operation of a meadow is an involution. In this paper, we study 'non-involutive meadows', i.e. variants of meadows ...
متن کاملDivision by Zero in Common Meadows
Common meadows are fields expanded with a total inverse function. Division by zero produces an additional value denoted with a that propagates through all operations of the meadow signature (this additional value can be interpreted as an error element). We provide a basis theorem for so-called common cancellation meadows of characteristic zero, that is, common meadows of characteristic zero tha...
متن کاملDivision by zero
For any sufficiently strong theory of arithmetic, the set of Diophantine equations provably unsolvable in the theory is algorithmically undecidable, as a consequence of the MRDP theorem. In contrast, we show decidability of Diophantine equations provably unsolvable in Robinson’s arithmetic Q. The argument hinges on an analysis of a particular class of equations, hitherto unexplored in Diophanti...
متن کاملInvolutive Division Technique: Some Generalizations and Optimizations
In this paper, in addition to the earlier introduced involutive divisions, we consider a new class of divisions induced by admissible monomial orderings. We prove that these divisions are noetherian and constructive. Thereby each of them allows one to compute an involutive Gröbner basis of a polynomial ideal by sequentially examining multiplicative reductions of nonmultiplicative prolongations....
متن کاملProbability Functions in the Context of Signed Involutive Meadows (Extended Abstract)
The Kolmogorov axioms for probability functions are placed in the context of signed meadows. A completeness theorem is stated and proven for the resulting equational theory of probability calculus. Elementary definitions of probability theory are restated in this framework.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Applied Logic
سال: 2015
ISSN: 1570-8683
DOI: 10.1016/j.jal.2014.10.001