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Errata for “Filters on Posets and Generalizations” [1]

Proposition 7: “Every co-brouwerian lattic e has least element” → “Every non-empty co-brouwerian

lattice has least element”.

Proof of theorem 17: (a \

∗

b) \

∗

c = {z ∈ A | a \

∗

b ⊆ c ∪ z } → (a \

∗

b) \

∗

c =

T

{z ∈ A | a \

∗

b ⊆ c ∪ z }.

Corollary 17: “F is an atomically separable” → “F is a tomically separable”.

Deﬁnition 38: “whenever

S

Z

S exists for S ∈ PA” → “whenever

S

Z

S exists for S ∈ PZ”.

Deﬁnition 39: “whenever

T

Z

S exists for S ∈ PA” → “whenever

T

Z

S exists for S ∈ PZ”.

Theorem 35: “for any F

0

,

, F

m

” → “for any F

0

,

, F

m

∈ F” .

Proof of t he orem 45: “taken into account the theorems 10 and 29” → “taken into account the

corollary 10 and theorem 23”.

Theorem 52: “a be prime” → “a is prime”.

Proof of theorem 52: “a is prime” → “a be prime”.

Theorem 54: “S ∩ ∂F

0” → “S ∩ ∂F

∅”.

Proof of theorem 56: “a ∪

F

b ∈ ⋆S” → “a ∪

F

b ∈ ⋆F” and “a ∈ ⋆S ∨ b ∈ ⋆S” → “a ∈ ⋆F ∨ b ∈ ⋆F”.

Proof of the ore m 59: “used the t heore ms 29 and 29” → “used theorem 29”; “used the theorems 23

and 10” → “used theorem 23 and corollary 10”.

Theorem 65: “which is an atomistic lattice” → “which is a c omplete atomisti c lattice”.

Theorem 68: “for every a, b ∈ A” → “for every a, b ∈ F”.

Proof of proposition 41: Replace all occurences of A → F.

Not yet pubished in IJPAM

Theorem 47: “distributive lattice with least element 0” → “distributive lattice with greatest element”

Proof of theorems 12: Messed ⊆ and ⊇.

Proof of theorem 55: card A → card T .

Proof of proposition 39: S → [S].

Proposition 13: atoms a ⊂ atoms b ⇒ a ⊂ b replace with a ⊂ b ⇒ atoms a ⊂ atoms b.

Proof of theorem 4.53: Should r ead “We have L ∩

A

F

0 ⇒ K

L

∩

Z

F

0 ⇒ L ∩

Z

F

0 ⇒ L ∩

A

F

0”.

Bib liography

[1] Victor Porton. Filters on posets and generalizations. International Journal of Pure and Applied Mathematics,

74(1):55–119, 2012.

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