# comprehension axiom in a sentence

1) Second-order semantics eliminates the need for the comprehension axiom, because these semantics imply that every possible set exists.

2) This holds because the set of comprehension axioms is a computable set (i.e., a recursive set).

axiom collocations
3) ACA0 is RCA0 plus the comprehension scheme for arithmetical formulas (which is sometimes called the "arithmetical comprehension axiom").

4) For example, one can take the theory ACA given by the Peano postulates together with comprehension axioms for first-order formulas only.

## comprehension axiom example sentences

5) As a general model, any model of analysis must of course satisfy all of the comprehension axioms; later we will consider weakening this requirement.

6) Moreover, a deductive calculus can be given for second-order logic (adapted from first-order logic and augmented by the comprehension axioms) that will be complete for the general semantics.

7) Thus a sentence is valid in the general semantics iff it is logically implied (in first-order logic) by the set of comprehension axioms.

8) In fact, ZFC actually does circumvent Russell's paradox by restricting the comprehension axiom to already existing sets by the use of subset axioms.

9) The deductive systems considered by Shapiro (1991) and Henkin (1950) add to the augmented first-order deductive scheme both comprehension axioms and choice axioms.

10) The initials "RCA" stand for "recursive comprehension axiom", where "recursive" means "computable", as in recursive function.

11) to be true in M . Call such sentences comprehension axioms .

12) Returning to the case where φ("n") is a formula with a free variable "n" and possibly other free variables, we define the comprehension axiom for φ to be:

These examples have been automatically selected and may contain sensitive content that does not reflect the opinions or policies of our website. Please inform us about the inappropriate sentences:
This site is designed to teach you English words in context with collocations with the help of example sentences.
You can easily memorize the word and the meaning of comprehension axiom
and This is a fast way of learning the meaning of comprehension axiom with example sentences.
Always focus on the learning on sentences with comprehension axiom
We believe you will easily learn to write and use the word comprehension axiom in a sentence.
You can practice spelling and usage of the word by getting 10 examples of sentences with comprehension axiom.
20 examples of simple sentences of comprehension axiom. We tried to find and publish the the words with Simple Sentences of comprehension axiom
Compound Sentences with comprehension axiom
Complex Sentences with comprehension axiom
Compound-Complex Sentences with comprehension axiom
in a sentence