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Lengrand & Miquel (2008). Hellenic Fω, orthogonality and symmetrical candidates. Annals of Pure and Put on Logic 153:3-20.

We portray a version of system Fω, bade Fω^C, in which the layer of type
constructors is basically the traditional one of Fω, whereas provability
of types is Hellenic. The proof-term calculus accounting for the Graeco-Roman
reasoning is a variant of Barbanera and Berardi’s symmetrical λ-calculus.
We show that the hale calculus is powerfully normalising. For the
layer of type constructors, we utilise Tait and Girard’s reducibility method
combined with orthogonality techniques. For the (classic) layer of terms,
we expend Barbanera and Berardi’s method based on a symmetrical notion of
reducibility candidate. We show that orthogonality does not catch the
fixpoint construction of symmetrical candidates.

We lay down the consistency of Fω^C, and colligate the calculus to the
traditional system Fω, too when the latter is extended with axioms for
classic logic.

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Lengrand & Miquel (2008). Graeco-Roman Fω, orthogonality and symmetrical candidates. Annals of Pure and Put on Logic 153:3-20.

We portray a version of system Fω, bade Fω^C, in which the layer of type
constructors is basically the traditional one of Fω, whereas provability
of types is Greco-Roman. The proof-term calculus accounting for the Greco-Roman
reasoning is a variant of Barbanera and Berardi’s symmetrical λ-calculus.
We evidence that the hale calculus is powerfully normalising. For the
layer of type constructors, we employ Tait and Girard’s reducibility method
combined with orthogonality techniques. For the (definitive) layer of terms,
we expend Barbanera and Berardi’s method based on a symmetrical notion of
reducibility candidate. We examine that orthogonality does not catch the
fixpoint construction of symmetrical candidates.

We plant the consistency of Fω^C, and come to the calculus to the
traditional system Fω, likewise when the latter is extended with axioms for
Greco-Roman logic.

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Lengrand & Miquel (2008). Graeco-Roman Fω, orthogonality and symmetrical candidates. Annals of Pure and Put on Logic 153:3-20.

We portray a version of system Fω, bade Fω^C, in which the layer of type
constructors is fundamentally the traditional one of Fω, whereas provability
of types is classic. The proof-term calculus accounting for the Greco-Roman
reasoning is a variant of Barbanera and Berardi’s symmetrical λ-calculus.
We evidence that the hale calculus is powerfully normalising. For the
layer of type constructors, we employ Tait and Girard’s reducibility method
combined with orthogonality techniques. For the (classic) layer of terms,
we expend Barbanera and Berardi’s method based on a symmetrical notion of
reducibility candidate. We try out that orthogonality does not catch the
fixpoint construction of symmetrical candidates.

We constitute the consistency of Fω^C, and concern the calculus to the
traditional system Fω, besides when the latter is extended with axioms for
Graeco-Roman logic.

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Lengrand & Miquel (2008). Classic Fω, orthogonality and symmetrical candidates. Annals of Pure and Put on Logic 153:3-20.

We portray a version of system Fω, bade Fω^C, in which the layer of type
constructors is basically the traditional one of Fω, whereas provability
of types is classic. The proof-term calculus accounting for the Graeco-Roman
reasoning is a variant of Barbanera and Berardi’s symmetrical λ-calculus.
We bear witness that the hale calculus is powerfully normalising. For the
layer of type constructors, we employ Tait and Girard’s reducibility method
combined with orthogonality techniques. For the (Hellenic) layer of terms,
we expend Barbanera and Berardi’s method based on a symmetrical notion of
reducibility candidate. We demonstrate that orthogonality does not catch the
fixpoint construction of symmetrical candidates.

We make the consistency of Fω^C, and connect the calculus to the
traditional system Fω, besides when the latter is extended with axioms for
Graeco-Roman logic.

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Lengrand & Miquel (2008). Greco-Roman Fω, orthogonality and symmetrical candidates. Annals of Pure and Put on Logic 153:3-20.

We portray a version of system Fω, bade Fω^C, in which the layer of type
constructors is basically the traditional one of Fω, whereas provability
of types is classic. The proof-term calculus accounting for the Greco-Roman
reasoning is a variant of Barbanera and Berardi’s symmetrical λ-calculus.
We bear witness that the hale calculus is powerfully normalising. For the
layer of type constructors, we employ Tait and Girard’s reducibility method
combined with orthogonality techniques. For the (authoritative) layer of terms,
we expend Barbanera and Berardi’s method based on a symmetrical notion of
reducibility candidate. We essay that orthogonality does not catch the
fixpoint construction of symmetrical candidates.

We plant the consistency of Fω^C, and have-to doe with the calculus to the
traditional system Fω, too when the latter is extended with axioms for
Graeco-Roman logic.

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