** Andronikos IV Palaiologos ( 1348 – 1385 )

** Philip IV ( 1285 – 1314 )

** Charles IV ( 1322 – 1328 )

** Henry IV ( 1589 – 1610 )

** Alphonse IV ( 1325 – 1357 )

** Ferdinand IV ( 1759 – 1806 )

** Louis IV ( 1715 – 1774 )

** Charles IV ( 1788 – 1808, 1808 )

** Hugh IV ( 1218 – 1272 )

** Odo IV ( 1315 – 1349 )

** John IV ( 1341 – 1345 )

** Francis IV ( 1524 – 1532 )

** John IV ( 1415 – 1427 )

** João IV ( 1640 – 1656 )

** Pedro IV ( 1826 )

** On the Terrors of Death ( Epistle IV )

** " Part IV: GPS heighting " SaLIS Vol.

** Philip IV the Fair, 1285 – 1314

** Charles IV the Fair, 1322 – 1328

** Henry IV the Great, 1589 – 1610

** Uruk IV period: 3300 – 3000 BC

** In the Star Trek: Voyager episode " One Small Step ", USS Voyager discovers the fate of Ares IV, one of the first manned expeditions to Mars in 2032.

** DNA Polymerase IV ( DinB ) – SOS repair polymerase

** IV.

** Conrad ( 1087 – 1098, nominal king under his father Henry IV )

** Eunectes murinus, the green anaconda, the largest species, is found east of the Andes in Colombia, Venezuela, the Guianas, Ecuador, Peru, Bolivia, Brazil and on the island of Trinidad.

** Eunectes notaeus, the yellow anaconda, a smaller species, is found in eastern Bolivia, southern Brazil, Paraguay and northeastern Argentina.

** Eunectes deschauenseei, the dark-spotted anaconda, is a rare species found in northeastern Brazil and coastal French Guiana.

** Eunectes beniensis, the Bolivian anaconda, the most recently defined species, is found in the Departments of Beni and Pando in Bolivia.

** Well-ordering theorem: Every set can be well-ordered.

** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.

** Trichotomy: If two sets are given, then either they have the same cardinality, or one has a smaller cardinality than the other.

** The Cartesian product of any family of nonempty sets is nonempty.

** König's theorem: Colloquially, the sum of a sequence of cardinals is strictly less than the product of a sequence of larger cardinals.

** Every surjective function has a right inverse.

** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.

** Hausdorff maximal principle: In any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.

** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.

** Antichain principle: Every partially ordered set has a maximal antichain.

** Every vector space has a basis.

** Every unital ring other than the trivial ring contains a maximal ideal.

** For every non-empty set S there is a binary operation defined on S that makes it a group.

** The closed unit ball of the dual of a normed vector space over the reals has an extreme point.

** Tychonoff's theorem stating that every product of compact topological spaces is compact.

** In the product topology, the closure of a product of subsets is equal to the product of the closures.

** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.

** Any union of countably many countable sets is itself countable.