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arithmetic logic unit αριθμητική λογική μονάδα
arithmetic logic unit

"on the foundations of logic and arithmetic," 129–38.
"on the foundations of logic and arithmetic," 129–38.

"subsystems of second order arithmetic", springer-verlag.
"subsystems of second order arithmetic", springer-verlag.

(Δες analytical hierarchy για την ανάλογη κατασκευή του second-order arithmetic.
(see analytical hierarchy for the analogous construction of second-order arithmetic.

Το παρών απαγωγικό σύστημα χρησιμοποιείται συνήθως στη μελέτη της second-order arithmetic.
this deductive system is commonly used in the study of second-order arithmetic.

kruskal's tree theorem, which has applications in computer science, is also undecidable from peano arithmetic but provable in set theory.
kruskal's tree theorem, which has applications in computer science, is also undecidable from peano arithmetic but provable in set theory.

υπολογισμός;αριθμητικός;επιστημονικός;οικονομικός;calculation;arithmetic;scientific;financial;
calculation;arithmetic;scientific;financial;

this corollary of the second incompleteness theorem shows that there is no hope of proving, for example, the consistency of peano arithmetic using any finitistic means that can be formalized in a theory the consistency of which is provable in peano arithmetic.
this corollary of the second incompleteness theorem shows that there is no hope of proving, for example, the consistency of peano arithmetic using any finitistic means that can be formalized in a theory the consistency of which is provable in peano arithmetic.

for example, the theory of primitive recursive arithmetic (pra), which is widely accepted as an accurate formalization of finitistic mathematics, is provably consistent in pa.
for example, the theory of primitive recursive arithmetic (pra), which is widely accepted as an accurate formalization of finitistic mathematics, is provably consistent in pa.

kirby and paris later showed goodstein's theorem, a statement about sequences of natural numbers somewhat simpler than the paris-harrington principle, to be undecidable in peano arithmetic.
kirby and paris later showed goodstein's theorem, a statement about sequences of natural numbers somewhat simpler than the paris-harrington principle, to be undecidable in peano arithmetic.

* allen, michael j.b., "nuptial arithmetic: marsilio ficino's commentary on the fatal number in book viii of plato's republic".
b., "nuptial arithmetic: marsilio ficino's commentary on the fatal number in book viii of plato's republic".