A ketrec nyitva marad, feltéve, hogy a háziállat nem szökik el.

A is the Hungarian definite article, meaning the.

• a ketrec = the cage
• a háziállat = the pet

Hungarian has two forms of the:

• a before consonant sounds
• az before vowel sounds

So:

• a ketrec
• az állat

Because ketrec is the subject of the sentence, so it stays in its basic dictionary form.

• A ketrec nyitva marad = The cage remains open

If it were the object, you might see ketrecet.
If it meant in the cage, you might see ketrecben.

Here, the cage is the thing doing the remaining open, so the plain form ketrec is used.

Nyitva means open in the sense of being in an open state.

In Hungarian, forms like nyitva, zárva, csukva are very common when describing a resulting state:

• Az ajtó nyitva van. = The door is open.
• A bolt zárva van. = The shop is closed.

So:

• nyitva marad = remains open

By contrast, nyitott is more like a regular adjective or past participle, and in many everyday situations Hungarian prefers nyitva for this kind of state.

Marad means remains or stays.

It comes from the verb maradni = to remain / to stay.

So:

• nyitva marad = remains open
• literally: stays open

This is a very common Hungarian structure:

• csendben marad = remains quiet
• otthon marad = stays home
• életben marad = stays alive / survives

Hungarian often uses the present tense where English uses will.

So A ketrec nyitva marad can naturally mean:

• The cage remains open
• The cage will remain open

The future is often understood from context. Hungarian can form an explicit future, but it does not need to here.

Feltéve, hogy means provided that, assuming that, or on condition that.

It introduces a condition.

So:

• feltéve, hogy a háziállat nem szökik el
• = provided that the pet does not escape

It is a fairly formal or neutral way to express a condition. In everyday speech, Hungarians may also use other conditional structures, but feltéve, hogy is completely correct and common in writing.

Yes, it functions as a fixed expression.

Literally, feltéve comes from the verb feltételez / related forms meaning to suppose / assume / posit, but learners should usually memorize feltéve, hogy as a set phrase meaning:

• provided that
• assuming that

So it is best learned as a chunk rather than analyzed word by word at first.

Because feltéve, hogy a háziállat nem szökik el is a subordinate clause or clause-like conditional phrase attached to the main statement.

Main clause:

• A ketrec nyitva marad = The cage remains open

Condition:

• feltéve, hogy a háziállat nem szökik el = provided that the pet does not escape

Hungarian often uses commas to separate such clauses, much like English.

Háziállat means pet or domestic animal.

It is made up of:

• házi = domestic, household
• állat = animal

So literally it is something like household animal or domestic animal, but in this sentence pet is the most natural translation.

Because nem is the standard Hungarian word for not.

• szökik el = escapes / runs away
• nem szökik el = does not escape / does not run away

Hungarian usually places nem directly before the verb or verbal unit it negates.

Szökik el is a verb plus a verbal prefix.

• szökik = escapes, runs away
• el = a verbal prefix that often adds the idea of away

Together:

• elszökik = escapes / runs away

In this sentence, because of negation, the prefix separates:

• positive: A háziállat elszökik.
• negative: A háziállat nem szökik el.

This is a very important Hungarian pattern: verbal prefixes often move away from the verb when something like negation or focus appears.

Yes, you will often meet the verb as elszökik.

But in actual sentences, the prefix may separate:

• elszökik = runs away
• nem szökik el = does not run away
• el fog szökni = will run away
• szökj el! = run away!

So learners should get used to the fact that Hungarian prefixed verbs can appear both joined and split.

Because in standard Hungarian, when a prefixed verb is negated, nem comes before the verb, and the prefix usually moves after it.

So:

• elszökik → nem szökik el

This is the normal rule for many prefixed verbs:

• bemegy = goes in

• nem megy be = does not go in

• kinyitja = opens it
• nem nyitja ki = does not open it

No. Szökik / elszökik can be used for a person, an animal, or even sometimes more figuratively.

For example:

• A rab megszökött. = The prisoner escaped.
• A kutya elszökött. = The dog ran away.

In your sentence, since it is about a háziállat, the sense is clearly run away / escape.

Hungarian often repeats nouns where English might use a pronoun, especially if it helps clarity.

So instead of:

• provided that it does not escape

Hungarian uses:

• feltéve, hogy a háziállat nem szökik el

This is completely natural. Hungarian does use pronouns, but it often prefers repeating the noun if that sounds clearer or more explicit.

Yes, Hungarian word order is flexible, but changes in order can change emphasis.

The given sentence is neutral and natural:

• A ketrec nyitva marad, feltéve, hogy a háziállat nem szökik el.

You could rearrange parts in some contexts, but that might sound more marked or emphasize a different element. For a learner, the original version is a good standard model.

A fairly literal translation would be:

• The cage stays open, provided that the pet does not escape away.

More natural English would be:

• The cage remains open, provided that the pet does not escape.
• The cage will remain open, provided that the pet doesn’t run away.

The most literal version helps show the Hungarian structure:

• A ketrec = the cage
• nyitva marad = stays/remains open
• feltéve, hogy = provided that
• a háziállat nem szökik el = the pet does not escape/run away

It sounds mostly neutral, with a slightly formal/written feel because of feltéve, hogy.

If someone wanted a more everyday spoken style, they might choose a different conditional wording. But this sentence is perfectly natural and correct, especially in instructions, rules, notices, or careful speech.

A rough English-style guide:

• ketrec ≈ KEH-trets
• nyitva ≈ NYIT-vaw
  (ny sounds a bit like the ny in canyon)
• marad ≈ MAW-rawd
• feltéve ≈ FEL-tay-veh
• hogy ≈ hodj or hody depending on how detailed you want to be
• háziállat ≈ HAA-zee-aa-llawt
• szökik ≈ SÖ-ki(k)
  (ö is like the vowel in German schön or French peu)
• el ≈ el

The stress in Hungarian is always on the first syllable of each word:

• KETrec
• NYITva
• MArad
• FELtéve
• HÁziállat
• SZÖkik