* W. J. Blok and Don Pigozzi, " Alfred Tarski's Work on General Metamathematics ", The Journal of Symbolic Logic, v. 53, No. 1 ( Mar., 1988 ), pp. 36 – 50.

* Tarski's Truth Definitions ( an entry of Stanford Encyclopedia of Philosophy )

* Stanford Encyclopedia of Philosophy entry on Tarski's Truth Definitions

The sentences whose existence is secured by the diagonal lemma can then, in turn, be used to prove fundamental limitative results such as Gödel's incompleteness theorems and Tarski's indefinability theorem.

Like other modern axiomatizations of Euclidean geometry, Tarski's employs a formal system consisting of symbol strings, called sentences, whose construction respects formal syntactical rules, and rules of proof that determine the allowed manipulations of the sentences.

Tarski's axioms, due to Alfred Tarski, are an axiom set for the substantial fragment of Euclidean geometry, called " elementary ," that is formulable in first-order logic with identity, and requiring no set theory.

Examples of early results from model theory applied to fields are Tarski's elimination of quantifiers for real closed fields, Ax's theorem on pseudo-finite fields, and Robinson's development of non-standard analysis.

Other often-used axiomizations of plane geometry are Hilbert's axioms and Tarski's axioms.

Another type of logics where Tarski's method is inapplicable are relevance logics, because given two theorems an implication from one to the other may not itself be a theorem in a relevance logic.

Because points are the only primitive objects, and because Tarski's system is a first-order theory, it is not even possible to define lines as sets of points.

* The 1997 Rolf Schock Prize in logic and philosophy from the Royal Swedish Academy of Sciences for his conceptually oriented logical works, especially the creation of domain theory, which has made it possible to extend Tarski's semantical paradigm to programming languages as well as to construct models of Curry's combinatory logic and Church's calculus of lambda conversion ; and

In the course of this he made several metamathematical discoveries, most notably Tarski's undefinability theorem using the same formal technique as Kurt Gödel used in his incompleteness theorems.

Tarski's lecture at the 1950 International Congress of Mathematicians in Cambridge ushered in a new period in which model-theoretic aspects were developed, mainly by Tarski himself, as well as C. C.

The T-schema or truth schema ( not to be confused with ' Convention T ') is used to give an inductive definition of truth which lies at the heart of any realisation of Alfred Tarski's semantic theory of truth.

Unlike the generalized solution to Tarski's circle-squaring problem, the axiom of choice is not required for the proof, and the decomposition and reassembly can actually be carried out " physically "; the pieces can, in theory, be cut with scissors from paper and reassembled by hand.

This approach to semantics is principally associated with Donald Davidson, and attempts to carry out for the semantics of natural language what Tarski's semantic theory of truth achieves for the semantics of logic ( Davidson 1967 ).

* Let us use the term “ deductive system ” as a set of sentences closed under consequence ( for defining notion of consequence, let us use e. g. Tarski's algebraic approach ).

Gödel also discovered the undefinability theorem in 1930, while proving his incompleteness theorems published in 1931, and well before the 1936 publication of Tarski's work ( Murawski 1998 ).

The National Firearms Act and Firearm Owners Protection Act define a " machine gun " in the United States code Title 26, Subtitle E, Chapter 53, Subchapter B, Part 1, § 5845 as:

§ 53, p. 1214 ;

In exceptional cases, universities were allowed to set longer average durations for certain subjects ( HGRP1995 § 26 ( 3 ), NHG2007 § 6 ( 3 ), HmbHG2001 § 53 ( 3 )).

The minimum municipal obligation is based on the latest actuarial valuation report prepared under the requirements of Chapter 2 of the act ( 53 P. S. § § 895. 201 — 895. 208 ).

The payroll used in determining the minimum municipal obligation of a pension plan under section 303 ( c ) of the act ( 53 P. S. § 895. 303 ( c )) shall be based on the payroll to be reported on the Internal Revenue Service Form W-2 and shall be the estimated payroll for the active membership of the pension plan, including projected increases in active membership, for the following plan year.

White dwarfs are thought to be the final evolutionary state of all stars whose mass is not high enough to become a neutron star — over 97 % of the stars in our galaxy .< sup >, § 1 .</ sup > After the hydrogen – fusing lifetime of a main-sequence star of low or medium mass ends, it will expand to a red giant which fuses helium to carbon and oxygen in its core by the triple-alpha process.

Absolutism was underpinned by a written constitution for the first time in Europe in the 1665 Kongeloven (" King's Law ") of Denmark-Norway, whose § 2 ordered that the monarch shall from this day forth be revered and considered the most perfect and supreme person on the Earth by all his subjects, standing above all human laws and having no judge above his person, neither in spiritual nor temporal matters, except God alone.

The opinion went on to state that Harvey's action under § 1983 " sought to invalidate a final state conviction whose lawfulness has in no way been impugned ".

" Exalted is He who took His Servant by night from al-Masjid al-îaram to al-Masjid al-Aq § a, whose surroundings We have blessed, to show him of Our signs.

§ 52. 002 ( 1984 ) ( directing clerk to issue an abstract of the judgment " on application of a person in whose favor a judgment is rendered "; no exception for superseded judgments ); Thulemeyer v. Jones, 37 Tex.

§ 1983 with Charles Lincoln being the lawyer who launched the case, alleging that the city violated her Fourth Amendment right to be free from unreasonable seizures by arresting her for a crime whose only punishment was a fine.

The second paragraph of Chapter 5 contains several articles of disparate administrative content ; but they are not the same as the " other prescripts " of § 1 ; the redaction of the headings is generally seen as confusing and infelicitous on this point.

" There is no definition of ' flash suppressor ' in § 265. 00, which contains all definitions for the ban, thus leaving grounds for arrest and prosecution uncertain until what is or is not a ' flash suppressor ' is resolved by state courts or clarified by statute.

" What exactly qualifies as comparable circumstances of captivity and treatment was never defined in Title 10, although the 38 USC § 101 ( 32 ) Veterans Affairs POW Status statute that served as the source of the ' comparability clause ' for the 1989 amendment to Title 10 contains similar language requiring " circumstances which the Secretary finds to have been comparable to the circumstances under which persons have generally been forcibly detained or interned by enemy governments during periods of war.

Although the caption of Texas Probate Code § 43 contains the phrase ' per stirpes ,' the distribution method described is actually what is known as " per capita with representation.

§ 53-244. 030, " Dwelling " means a residential structure that contains one to four units, whether or not that structure is attached to real property.

§ 29 contains three words that were suppressed by Nietzsche's sister in 1895.

For example, German philosopher Friedrich Nietzsche argued, in the § 133 of his The Dawn, that in such cases compassionate impulses arise out of the projection of our identity unto the object of our feeling.

cos ( nx ) + i sin ( nx ) and the Bessel function identity ( See Abramowitz and Stegun § 9. 6. 19 ):

In Europe, the § is called the paragraph symbol ( or token, or sign ).

It is frequently used along with the pilcrow (¶), or paragraph sign ( which is what § is called in Europe ).

work also discusses Ashby's 1000-switch example ; see § C1. 2.

McManus ( 1991, § 3. 15 ) discusses possible etymologies of all the letter names, and as well as the five mentioned above, he adds one other definite tree name: onn " ash " ( the Auraicept wrongly has furze ).

34 " discusses the symbolic and representational meaning of water utilized in Cicero ’ s Pro Caelio, § 34.