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  • Reverse mathematics
  • countable well ordering starting with any set. ATR0 is equivalent over ACA0 to the principle of Σ1 1 separation. ATR0 is impredicative, and has the proof-theoretic

  • Kruskal's tree theorem
  • prominent example in reverse mathematics as a statement that cannot be proved in ATR0 (a second-order arithmetic theory with a form of arithmetical transfinite

  • Proof theory
  • increasing strength, these systems are named by the initialisms RCA0, WKL0, ACA0, ATR0, and Π1 1-CA0. Nearly every theorem of ordinary mathematics that has been

  • ATR
  • linguistics Atractyloside, a toxin and inhibitor of "ADP/ATP translocase" ATR0, an axiom system in reverse mathematics Answer to reset, a message output

  • Gödel's incompleteness theorems
  • tree theorem (or its finite form) is undecidable in a much stronger system ATR0 codifying the principles acceptable based on a philosophy of mathematics

  • Laver's theorem
  • _{1}^{1}} -CA0 and ATR0, and to be weaker than Π 1 1 {\displaystyle \Pi _{1}^{1}} -CA0. However, it remains open whether it is equivalent to ATR0 or strictly

  • Large countable ordinal
  • element begins. For an example of a recursive pseudo-well-ordering, let S be ATR0 or another recursively axiomatizable theory that has an ω-model but no hyperarithmetical

  • Ordinal analysis
  • (shown by Gentzen using cut elimination). ACA0, arithmetical comprehension. ATR0, arithmetical transfinite recursion. Martin-Löf type theory with arbitrarily

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Astrological/horoscope meaning of atr0. atr0 means: undefined

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    A: Meaning of A in the acronym atr0 means: The letter A has two bars connected at a pointed edge and a cross bar holding them together. From an open end to a pointed edge signifies that all energies are trained to a point to achieve the most singularly important goal. The cross bar shows caution. Failure is avoided by stringing all required resources together. A also looks like a Pyramid with the peak as the apex of the Pyramid. Pyramids are iconic. A therefore symbolizes prominence and a desire to be recognized for ones achievements. The cross bar also represents a rung in ladder. To get to the top, one has to first step on the rung. It also means originality, a strong will power and an enterprising ability. The upper-case version consists of the two slanting sides of a triangle, crossed in the middle by a horizontal bar. It shows aspiration, the dominance to be successful, positive attitude, an optimistic world view and egotism.

    T: Meaning of T in the acronym atr0 means: T is a vertical strand crossed at the top by a horizontal strand. With the top strand balanced in the middle by the vertical strand, T shows balance and stability in its ways. It is also forgoing and spiritual. With the top strand projected up by the bottom strand, T is highly ambitious, but also kind to others as it can let others rest on its horizontal top. This makes T selfless, cooperative, womanly and dutiful. It also displays a high degree of generosity and liberalism.

    R: Meaning of R in the acronym atr0 means: Letter R sits comfortably on two legs that are a litlle spread apart. It displays great strength. It's close top to itself is uncaring, impetuous, and insensitive.

    0: Meaning of 0 in the acronym atr0 means: undefined

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